Vector Bundles

[DeRhamSource]

Implementation of topological and differentiable vector bundles over manifolds.

Features:

• abstract vector bundles on topological manifolds
• trivializations
• local frames
• simple sections
• vector bundle fibers
• differentiable vector bundles and tensor bundles

Improvements in the preexisting code

• restriction of vectorframes depended on some strange order: fixed!
• SR enforcement for automorphism field inversion removed (due to ticket prefer "X in Fields()" rather than "X.is_field()" #28189)
• is_unit() method superficially implemented for scalar fields to ensure division free matrix inversion for changes of frames (may be removed when Automorphism fields: remove SR enforcement when computing the inverse #28629 is solved)

Planned in the farther future

• sections of general tensor products and automorphism fields on vector bundles
• tensor products and Whitney sums of vector bundles
• better zero treatment as in Tensor Fields: Better Zero Treatment #28562
• TensorField inherits from Section, VectorFrame inherits from LocalFrame
• total space comes with induced charts

Depends on #28189

CC: @tscrim @egourgoulhon

Component: geometry

Keywords: vector bundles

Author: Michael Jung

Branch/Commit: 4ae4ca3

Reviewer: Eric Gourgoulhon, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/28159

[DeRhamSource]

Author: Michael Jung

[DeRhamSource]

Changed keywords from none to vector bundles

[DeRhamSource]

Branch: u/gh-DeRhamSource/vector_bundles

[DeRhamSource]

comment:4

Please take a short look and give me a short feedback. I want to know whether I'm on the right way or not.

Furthermore, I appreciate tricks and advices. Thanks in advance! :)

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New commits:

5d5520d

Basic structure

[DeRhamSource]

Commit: 5d5520d

[DeRhamSource]

Description changed:

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+Implementation of topological and differentiable vector bundles over manifolds.

[egourgoulhon]

comment:6

Replying to @DeRhamSource:

Please take a short look and give me a short feedback. I want to know whether I'm on the right way or not.

Furthermore, I appreciate tricks and advices. Thanks in advance! :)

Thanks for this endeavor. I gave a look: it looks very nice! Please go on.

A minor comment: for class names, full names are preferable, so TopolVectorBundle could be replaced by TopologicalVectorBundle. Also maybe, in the context of vector bundles, TransitionMap is more appropriate than CoordChange.

[DeRhamSource]

comment:7

Thanks!

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

ed60a5d

Trivializations almost finished